2021 Fall AMC 10B Problems/Problem 1

Revision as of 21:55, 22 November 2021 by Kingofpineapplz (talk | contribs) (Solution 1)

Problem

What is the value of $1234+2341+3412+4123?$

$(\textbf{A})\: 10{,}000\qquad(\textbf{B}) \: 10{,}010\qquad(\textbf{C}) \: 10{,}110\qquad(\textbf{D}) \: 11{,}000\qquad(\textbf{E}) \: 11{,}110$

Solution 1

We see that $1, 2, 3,$ and $4$ each appear in the ones, tens, hundreds, and thousands digit exactly once. Since $1+2+3+4=10$, we find that the sum is equal to \[10\cdot(1+10+100+1000)=\boxed{(\textbf{E})11,110}.\]


Note: it is equally valid to manually add all 4 numbers together to get the answer.


~kingofpineapplz